Alas, the MIDI is stored within a PianoDiary SQLite database and not as a midi file. So, no easy way to export and import.
Unable to get the PianoDiary app WiFi or Bluetooth working with a MAC so now I explore hard wiring from iPhone 5s to a MAC.

I could then press PLAY on the iPhone 5S and RECORD on the MAC to export from the iPhone and vice versa to import.
Is there any good reason why this hardwire approach wouldn't work using the Apple Camera connection kit ?
Is there a better way to do this connection via cable ? (I have given up on WiFi and Bluetooth)